Question: 12 Let (A1, A2, A3, ...) be a sequence of events. Prove that if the series = P(A) converges, then P (UA) = 0. This

12 Let (A1, A2, A3, ...) be a sequence of events. Prove that if the series = P(A) converges, then P (UA) = 0. This is called the Borel-Cantelli lemma. It says that if P(A)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

A commercial 3D printer is purchased for $300,000. The salvage value of the printer decreases by 40% each year that it is held. The cost to operate and maintain the machine the first year it is used...

12. Let{A1, A2, A3,...} be a sequence of events. Prove that if the series/ n=1 P (An) converges, then P * ) m=1 ( n=m An , = 0. This is called the Borel-Cantelli lemma. It says that if / n=1 P (An)

28. Let A1, A2, A3, ... be a sequence of events of a sample space. Prove that P *+ n=1 An , . n=1 P (An). This is called Booles inequality.

42. Let A1, A2, A3, . . . be a sequence of events of a sample space. Prove that P [ n=1 An X n=1 P(An). This is called Booles inequality.

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

Change issue 16 in portion 4.2 of your substance, including drawing markers from a compartment of markers with ink and markers without ink. Expect that the case contains 19 markers: 14 that contain...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

The director of a not-for-profit organization was overheard saying that government auditing standards (GAGAS) were developed by the federal government to ensure that local governments were spending...

Kiran is appointed as a Life Insurance Agent in a renowned Insurance company. In order to acquire and expand her client base she is required to prepare a presentation on the needs for buying the life...

uantitative easing Question 33 Select one: a. floods the financial system with debt. b. creates risks of inflation as the economy approaches potential GDP. c. replaces liabilities on chartered bank...

Draw all constitutional isomers with molecular formula C 4 H 11 N, and provide a name for each isomer.